WASHINGTON—The Obama administration is fashioning a new strategy to prosecute Syrian war crimes based on a trove of photos smuggled out of the country by the defector code-named Caesar, U.S. officials said.

Because Russia, the primary patron of Syrian President Bashar al-Assad, has blocked an international prosecution, the U.S. and its allies are focusing on possible crimes where individual countries already have jurisdiction—those involving their own nationals or dual citizens who may have been victims or perpetrators in...